How do I prove that tan^4theta - sec^4theta = -2tan^2 -1

Question

I need to prove the above trig function.

Answer 1

make theta = x.... cause it is simpler to type

sec^4(x) = (1+ tan^2(x))^2 = 1+2tan^2(x) +tan^4(x)

therefore left hand side=tan^4-(1+2tan^2(x)+tan^4(x))

= tan^4(x)-1-2tan^2(x)-tan^4(x)

=-1-2tan^2(x)=-2tan^2(x)-1=right hand side ^___^

Answer 2

opps nearly forgot  Sec^2(x)= 1+tan^2(x) is an identity it is a pythagoras relationship  in trigonometry ^___^